What I would suggest:
- Use an external drive (USB is fine)
- Create a cloned backup of the old Mac using either CarbonCopyCloner or SuperDuper
- When the new Mac comes, connect the cloned backup and press the power-on button
- Begin setup. When setup assistant asks if you wish to migrate from another Mac or drive, YES, you want to do this
- "Aim" setup assistant at the cloned backup
- Select those items you wish to be migrated.
- Let setup assistant "do its thing".
- You'll eventually be presented with a login screen. Login, and it should "look just like the old one did"...